1. Field of the Invention
The present invention generally relates to methods for characterizing a sample of porous media using at least one measuring device along with a multipoint statistical (MPS) model. In particular, the invention relates to a method for characterizing flow properties of the sample whereby flow simulation models are generated from one or more set of reflected measured data provided by the at least one measuring tool in combination with the MPS model.
2. Background of the Invention
The principle of confocal imaging was patented by Marvin Minshy in 1957 (see U.S. Pat. No. 3,013,467 dated Nov. 7, 1957 issued to Marvin Minshy). In a conventional fluorescence microscope, the sample is flooded in light from a light source. Due to the aspects of light intensity traveling over a distance, all parts of the sample throughout the optical path will be excited and the fluorescence detected by a photodetector.
However, confocal microscope uses point illumination and a pinhole in an optically conjugate plane in front of the detector to eliminate out-of-focus information. Only the light within the focal plane can be detected, so the image quality is much better than that of wide-field images. As only one point is illuminated at a time in confocal microscopy, 2D or 3D imaging requires scanning over a regular raster (i.e. a rectangular pattern of parallel scanning lines) in the specimen. The thickness of the focal plane is defined mostly by the inverse of the square of the numerical aperture of the objective lens, and also by the optical properties of the specimen and the ambient index of refraction. These microscopes also are able to see into the image by taking images at different depths (see Wikipedia (2009)).
In particular, confocal microscopy is widely used in the life sciences and semiconductor industries (see Stevens, J. K., Mills, L. R., and Trogadis, J. E., 1994, Three-dimensional confocal microscopy: Volume investigation of biological specimens: Academic Press, San Diego, Calif., 506 p.; Matsumoto, B., 2002, Cell biological applications of confocal microscopy: Academic Press, San Diego, Calif., 2nd edition, 499 p.; Pawley, J. B., 2006, Handbook of biological confocal microscopy: Springer, New York, N.Y., 3rd edition, 985 p.; Nikon, 2009, http://www.microscopyu.com/articles/confocal/index.html, accessed on March 30; and Olympus, 2009a, http://www.olympusconfocal.com/theory/confocalintro.html, accessed on March 30). FIG. 1 shows the basic principles of confocal microscopy, In particular, FIG. 1 shows features that include detector pinhole and parallel focal planes at different levels in the specimen (see Olympus (2009a)).
FIG. 2 provides a comparison of conventional widefield (left) vs. confocal (right) microscopy. Further, FIG. 3 shows images of biological specimens that show a comparison between conventional widefield (top) vs. confocal (bottom) microscopy. From Olympus (2009a). It is noted that the the confocal image is a high-resolution measurement of a single focused point on the specimen. From Olympus (2009a). Further, it is noted confocal microscopy is not commonly used in the earth sciences. Fredrich et al. (1995) and Fredrich (1999) created 3D images of rocks using transmitted laser confocal microscopy (see Fredrich, J. T., 1999, 3D imaging of porous media using laser scanning confocal microscopy with application to microscale transport processes: Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, v. 24, Issue 7, p. 551-561; and Fredrich, J. T., Menendez, B., and Wong, T. F., 1995, Imaging the pore structure of geomaterials: Science, v. 268, p. 276-279). O'Connor and Fredrich (1999) did flow experiments on these numerical rocks using lattice-Boltzmann methods (see O'Connor, R. M., and Fredrich, J. T., 1999, Microscale flow modeling in geologic materials: Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy, v. 24, Issue 7, p. 611-616). Li and Wan (1995) used confocal laser microscopy to image asphaltene particles (see Li, H., and Wan, W. K., 1995, Investigation of the asphaltene precipitation process from Cold Lake bitumen by confocal scanning laser microscopy: SPE Preprint 30321, Presented at the International Heavy Oil Symposium, Calgary, Alberta, Canada, June 19-21).
White-Light Confocal Profilometers are commercially available, and are mainly used to study surface roughness of industrial materials. As an example, the Nanovea ST400 Profiler from Microphotonics (2009) measures fine-scale topography of a surface using white-light non-contacting confocal profilometry. Various probes are available, each with a different spot size, vertical resolution, and depth of field.
Mell (2006) stated that, “The axial chromatism technique uses a white light source, where light passes through an objective lens with a high degree of chromatic aberration (see Mell, B., Analytical report Nanovea—061213-21: Microphotonics internal report, 10 p., 2006). The objective lens' refractive index will vary in relation to the wavelength of the light. In effect, each separate wavelength of the incident white light will refocus at a different distance from the lens (different height). When the measured sample is within the range of possible heights, a single monochromatic point will be focalized and form the image. Due to the confocal configuration of the system only the wavelength in focus will pass through the spatial filter with high efficiency, thusly causing all other wavelengths to be out of focus.”
Laser Confocal Profilometry or laser confocal microscopes are commercially available, and are mainly used for metrology, i.e., the measurement of industrial materials. As an example, the Olympus (2009b) LEXT OLS3000 confocal laser scanning microscope measures fine-scale topography of surfaces using non-contact laser profilometry. Resolution is a function of the objective lens. The device uses a purple semiconductor laser with a wavelength of 408 nm.
Pore-Size Distribution
Pore-Size Distribution can be defined in at least one aspect as variations in pore sizes in reservoir formations, wherein each type of rock has its own typical pore size and related permeability.
For example, referring to FIG. 4, carbonate rocks have pore sizes that range over at least 9 orders of magnitude, from km-scale caves to micropores at submicron-scale. Pores are subdivided into pore bodies and pore throats. In particular, FIG. 4 illustrates a pore network consisting of a pore body and connected pore throats. In numerical pore-network models, pore bodies are spherical in shape and pore throats are circular, rectangular, or triangular in cross section.
FIG. 5 shows pore bodies and pore throats that can be subdivided into macro-, meso- and micropores following the definition of Marzouk et al. (1995), as implemented on borehole log data (Hassall et al., 2004; Gomaa et al., 2006) for pore throats, and Tanprasat (2005) for pore bodies (see Marzouk, I., Takezaki, H., and Miwa, M., 1995, Geologic controls on wettability of carbonate reservoirs, Abu Dhabi, U.A.E.: SPE Preprint 29883, Presented at the Middle East Oil Show, March 11-14; Hassall, J. K., Ferraris, P., Al-Raisi, M., Hurley, N. F., Boyd, A., and Allen, D. F., 2004, Comparison of permeability predictors from NMR, formation image and other logs in a carbonate reservoir: SPE Preprint 88683, Presented at 12th Abu Dhabi International Petroleum Exhibition and Conference, October 10-13; Gomaa, N. M., Allen, D. F., Zammito, S., Okuyiga, M. O., Azer, S. R., Ramamoorthy, R., and Bize, E., 2006, Case study of permeability, vug quantification, and rock typing in a complex carbonate: SPE Preprint 102888, presented at 81st, Annual Technical Conference and Exhibition, September 24-27; and Tanprasat, S. J., 2005, Petrophysical analysis of vuggy porosity in the Shu'aiba formation of the United Arab Emirates: MSc thesis, Colorado School of Mines, Golden, Colo., 190 p.).
It is noted that pore-size distributions are typically shown as histograms of frequency vs. radius. Radius is generally 2D, and can be determined using various image-analysis approaches. Examples of such approaches are:                1) Core-slab photography—This technique, summarized by Hurley et al. (1998; 1999), involves coating core slabs with water-soluble, fluorescent paint. Photos taken under black light are processed using image-analysis software to determine 2D pore-size distributions (see Hurley, N. F., Zimmermann, R. A., and Pantoja, D., 1998, Quantification of vuggy porosity in a dolomite reservoir from borehole images and core, Dagger Draw field, New Mexico: SPE 49323, presented at the 1998 Annual Conference and Exhibition, New Orleans, La., September, 14 p. Jennings, J. B., 1987, Capillary pressure techniques: Application to exploration and development geology: AAPG Bulletin, v. 71, p. 1196-1209; and Hurley, N. F., Pantoja, D., and Zimmermann, R. A., 1999, Flow unit determination in a vuggy dolomite reservoir, Dagger Draw field, New Mexico: Paper GGG, SPWLA 40th Annual Logging Symposium, Oslo, Norway, May 30-June 3, 14 p.).        2) Petrographic image analysis—This technique, summarized by Anselmetti et al. (1998), involves image analysis of thin sections. The smallest pores are generally the thickness of a thin section. The largest pores are constrained by the area of the scan (see Anselmetti, F. S., Luthi, S., and Eberli, G. P., 1998, Quantitative characterization of carbonate pore systems by digital image analysis: AAPG Bulletin, v. 82, p. 1815-1836).        
Pore-size distributions can also be determined from methods that deal with bulk-rock samples. Examples are:                1) Mercury injection capillary pressure (MICP). Referring to FIG. 6, this technique, summarized by Jennings (1987) and Pittman (1992), involves progressive injection of mercury into a rock at higher and higher pressures (see Jennings, J. B., 1987, Capillary pressure techniques: Application to exploration and development geology: AAPG Bulletin, v. 71, p. 1196-1209; and Pittman, E. D., 1992, Relationship of porosity and permeability to various parameters derived from mercury injection-capillary pressure curves for sandstone: AAPG Bulletin, v. 76, p. 191-198). At each increased pressure step, pore throats of a particular size are invaded by mercury. Mercury invades all pore bodies connected to the outside of the core plug and pore throats of the size that are currently being invaded. MICP is not useful for some pore throats because these throats are filled at very low injection pressures. Pore-throat size distributions are generally shown as histograms, which are computed from MICP results (FIG. 6). In particular, FIG. 6 shows pore-throat size distribution from conventional mercury injection capillary pressure (MICP) data for a carbonate rock sample. The conventional MICP results are converted to the radius of the pore throats (x axis) and the volumes of both pore throats and connected pore bodies (y axis), i.e., r vs. (v+V) in FIG. 4.        2) Constant rate mercury injection (CRMI). Referring to FIG. 7, this technique maintains a constant injection rate and monitors fluctuations of the injection pressure (see Yuan, H. H. and B. F. Swanson, 1989, Resolving pore-space characteristics by rate-controlled porosimetry: SPE Formation Evaluation, v. 4, p. 17-24). The injection rate is kept extremely low so that the pressure loss due to flow inside the sample is negligible compared to the capillary pressure. In this case, the observation of a sudden pressure drop is the result of the movement of mercury from pore throats into pore bodies, and is accompanied by mercury instantaneously filling the pore bodies (FIG. 7). In particular, FIG. 7(A) shows CRMI injection pressure vs. volume results for a Berea sandstone sample of 1.5 mL volume (adapted from Chen and Song, 2002 (see Chen, Q., and Song, Y.-Q., 2002, What is the shape of pores in natural rocks?: Journal of Chemical Physics, v. 116, p. 8247-8250)). P(R) is the capillary pressure of a pore body with radius of R and this pore body is connected by a pore throat with capillary pressure of p and radius of r (P<p, R>r). Further, FIG. 7(B) shows CRMI capillary-pressure curves for a Berea sandstone sample (modified from Yuan and Swanson, 1989). Conventional MICP provides the total capillary-pressure curve, whereas CRMI provides pore-body and pore-throat capillary-pressure curves. The further rise of injection pressure corresponds to the filling of pore throats with smaller radius. The volume of pore bodies can be determined from the injection rate and the time it takes to fill the pore bodies. Therefore, CRMI provides the conventional MICP curve, and it also provides the size distributions of pore bodies and pore throats.        3) Micro-CT scans. Referring to FIG. 8, this technique, summarized in Knackstedt et al. (2004), uses x-ray computed tomography (CT) on small samples (commonly 5-mm diameter core plugs) to detect pore bodies (see Knackstedt, M. A., Arns, C. H., Sakellariou, A., Senden, T. J., Sheppard, A. P., Sok, R. M., Pinczewski, W. V., and Bunn, G. F., 2004, Digital core laboratory: Properties of reservoir core derived from 3d images: SPE Preprint 87009, Presented at the Asia-Pacific Conference on Integrated Modelling for Asset Management, March 29-30). Software converts physical pore images into pore-network models, with their resulting pore-body and pore-throat size distributions (FIG. 8). In particular, FIG. 8 shows a physical pore network showing pores in green (left) generated from microCTscan, and pore-network model (right). The size of the cube on the left is 3 mm on each side. On the right, the balls represent pore bodies and the sticks represent pore throats.        4) Nuclear magnetic resonance (NMR). This technique, summarized by Coates et al. (1999), is based on the interaction of hydrogen nuclei (protons) with a magnetic field and pulses of radio-frequency signals (see Coates, G. R., Xiao, L. and Prammer, M. G., 1999, NMR logging: Principles and applications: Halliburton Energy Services, USA, 234 p.). The NMR transverse relaxation time distribution (T2 distribution) is mostly related to pore-size distribution in the rock, although transverse relaxation is also related to factors such as surface relaxivity and fluid type. Research has shown that grain-surface relaxation has the most important influence on T2 relaxation times for rocks. Surface relaxivity (ρ) is a measure of the ability of grain surfaces to cause nuclear-spin relaxation. Different rocks have different surface-relaxivity characteristics. The rate of proton grain-surface relaxation depends on how often protons collide with or get close enough to interact with grain surfaces. As a result, the surface to volume (S/V) ratio of rock pores significantly influences NMR relaxation times. For spherical pores, S/V is proportional to the inverse of the pore radius. Larger pores have therefore relatively smaller S/V ratios and proportionally longer relaxation times. Smaller pores have relatively larger S/V ratios, resulting in shorter relaxation times. NMR surface relaxivity is characterized by the following equations:        
            (              1                  T          2                    )        s    =            ρ      ⁢              S        V            ⁢                          ⁢      and      ⁢                          ⁢                        (                      1                          T              2                                )                s              =                  ρ        e            ⁢      r                      where ρ is surface relaxivity in units of μ/s, S is surface area (μ2), V is volume (μ3), ρe is effective relaxivity (μ/s), and r is radius (μ). Thus, we can obtain pore-size distribution information from NMR T2 distributions.        
Multipoint Statistics
Multipoint (or multiple-point) statistical methods (MPS) are a new family of spatial statistical interpolation algorithms proposed in the 1990s that are used to generate conditional simulations of discrete variable fields, such as geological facies, through training images (see Guardiano, F., and Srivastava, R. M. 1993, Multivariate geostatistics: Beyond bivariate moments: Geostatistics-Troia, A. Soares. Dordrecht, Netherlands, Kluwer Academic Publications, v. 1, p. 133-144). MPS is gaining popularity in reservoir modeling because of its ability to generate realistic models that can be constrained by different types of data. Unlike the conventional 2-point or variogram-based geostatistical approaches, MPS uses a training image to quantify the complex depositional patterns believed to exist in studied reservoirs. These training patterns are then reproduced in the final MPS models with conditioning to local data collected from the reservoirs. Therefore, MPS allows modelers to use their prior geological interpretations as conceptual models (training images) in the reservoir modeling process and to evaluate the uncertainty associated with the prior interpretations by using different training images.
In addition to categorical variables, MPS can also be used to deal with continuously variable training images, such as spatial distribution of porosity. Two families of MPS algorithms are available to handle these different types of training images: Snesim for categorical variables and Filtersim for continuous variables. Strebelle (2002) proposed an efficient Snesim algorithm that introduced the concept of a search tree to store all replicates of patterns found within a template over the training image (see Strebelle, S. 2002, Conditional simulation of complex geological structures using multiple point statistics: Mathematical Geology, v. 34, p. 1-22).
This makes Snesim code several orders of magnitude faster than the original algorithm proposed by Guardiano and Srivastava (1993). Filtersim, developed by Zhang (2006), applies a set of local filters to the training image, which can be either categorical or continuous, to group local patterns into pattern classes (see Zhang, T. 2006, Filter-based training image pattern classification for spatial pattern simulation. PhD dissertation, Stanford University, Palo Alto, Calif.). Pattern simulation then proceeds on the basis of that classification.
Snesim and Filtersim algorithms honor absolute, or “hard” constraints from data acquired in wells or outcrops, and other interpreted trend maps of the reservoir under study. Training images are the main driver of any MPS approach. An issue raised implicitly by current MPS algorithms is how to generate training images. Training images are supposed to model or reproduce real geological features and should as much as possible be derived from existing geologically meaningful images. This requires research on statistical and image-processing methods that will allow use of images from any source: hand-drawn sketches, aerial photographs, satellite images, seismic volumes, geological object-based models, physical-scale models, or geological process-based models.
Categorically variable training images are easier to generate than continuously variable training images. An object-based approach is commonly used to generate training images with categorical variables. A region-based approach, combined with the addition of desired constraints, can be used to generate continuously variable training images (Zhang et al., 2006).
U.S. Pat. No. 4,702,607 discusses a three dimensional structure viewer of a transparent object, but does not discuss porous media. Further, U.S. Pat. Nos. 6,288,782, 6,661,515, and 7,384,806 discuss the use of confocal microscopy to find defects on semiconductor wafers, however the shapes, volumes, or surface areas of such defects are not quantified. Further still, U.S. Pat. No. 6,750,974 discusses 3D imaging of droplets, however it does not disclose porous media. It is further noted that U.S. Pat. Nos. 7,092,107 and 7,230,725 provide a method to determine the 3D topology of objects, with a focus on teeth, however it does not discuss porous media.
Therefore, there is a need for methods and devices that overcome the above noted limitations of the prior art. By non-limiting example, devices and methods that can provide a quantitative evaluation of 3D pore-size distributions using 2D digital images by confocal profilometry scanning of rock samples. Further, there is a need for methods and devices that overcome the above noted limitations of the prior art that can use non-contacting white-light and laser confocal profilometry a method to quantify discrete pore shapes, volumes, and surface areas in porous media.